/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 23 In which of the following decays... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 44: Problem 23

In which of the following decays are the three lepton numbers conserved? In each case, explain your reasoning. (a) \(\mu^-\rightarrow e^- + \nu_e + \overline{\nu}_\mu\); (b) \(\tau^-\rightarrow e^- + \overline{\nu}_e + \overline {\nu} _\tau\); (c) \(\pi^+ \rightarrow e^+ + \gamma\); (d) \(n \rightarrow p + e^- + \overline{\nu}_e\).

Short Answer

Expert verified
Decays (a), (b), and (d) conserve lepton numbers. Decay (c) does not.

Step by step solution

01

Understand Lepton Number Conservation

Lepton number conservation states that in any nuclear or particle reaction, the sum of the lepton numbers before the reaction must equal the sum after the reaction. There are three types of lepton numbers: electron lepton number \(L_e\), muon lepton number \(L_\mu\), and tau lepton number \(L_\tau\). These numbers must be independently conserved in a reaction.
02

Evaluate Decay (a) \(\mu^-\rightarrow e^- + \nu_e + \overline{\nu}_\mu\)

Assign lepton numbers to each particle: \(\mu^-, L_e = 0, L_\mu = 1, L_\tau = 0\); \(e^-, L_e = 1, L_\mu = 0, L_\tau = 0\); \(u_e, L_e = 1, L_\mu = 0, L_\tau = 0\); \(\overline{u}_\mu, L_e = 0, L_\mu = -1, L_\tau = 0\). Before decay: \(L_e = 0, L_\mu = 1, L_\tau = 0\). After decay: \(L_e = 1 + 1, L_\mu = 0 - 1, L_\tau = 0\). All lepton numbers are conserved.
03

Evaluate Decay (b) \(\tau^-\rightarrow e^- + \overline{\nu}_e + \overline{\nu}_\tau\)

Assign lepton numbers to each particle: \(\tau^-, L_e = 0, L_\mu = 0, L_\tau = 1\); \(e^-, L_e = 1, L_\mu = 0, L_\tau = 0\); \(\overline{u}_e, L_e = -1, L_\mu = 0, L_\tau = 0\); \(\overline{u}_\tau, L_e = 0, L_\mu = 0, L_\tau = -1\). Before decay: \(L_e = 0, L_\mu = 0, L_\tau = 1\). After decay: \(L_e = 1 - 1, L_\mu = 0, L_\tau = 0 - 1\). All lepton numbers are conserved.
04

Evaluate Decay (c) \(\pi^+ \rightarrow e^+ + \gamma\)

Assign lepton numbers to each particle: \(\pi^+, L_e = 0, L_\mu = 0, L_\tau = 0\); \(e^+, L_e = -1, L_\mu = 0, L_\tau = 0\); \(\gamma, L_e = 0, L_\mu = 0, L_\tau = 0\). Before decay: \(L_e = 0, L_\mu = 0, L_\tau = 0\). After decay: \(L_e = -1, L_\mu = 0, L_\tau = 0\). Lepton numbers are not conserved.
05

Evaluate Decay (d) \(n \rightarrow p + e^- + \overline{\nu}_e\)

Assign lepton numbers to each particle: \(n, L_e = 0, L_\mu = 0, L_\tau = 0\); \(p, L_e = 0, L_\mu = 0, L_\tau = 0\); \(e^-, L_e = 1, L_\mu = 0, L_\tau = 0\); \(\overline{u}_e, L_e = -1, L_\mu = 0, L_\tau = 0\). Before decay: \(L_e = 0, L_\mu = 0, L_\tau = 0\). After decay: \(L_e = 1 - 1, L_\mu = 0, L_\tau = 0\). All lepton numbers are conserved.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Muon Decay
The muon, denoted as \(\mu^-\), is a type of lepton, which is similar to an electron but much heavier. In the decay process, a muon can transform into other particles.
In the decay \(\mu^-\rightarrow e^- + u_e + \overline{u}_\mu\), the muon decays into:
  • an electron \((e^-)\),
  • an electron neutrino \((u_e)\), and
  • a muon antineutrino \((\overline{u}_\mu)\).
Lepton number conservation must be obeyed, meaning the sum of lepton numbers must be the same before and after the decay. For this reaction:
  • Electron lepton number \( (L_e) \) starts at 0 and ends at 1 (electron) + 1 (electron neutrino) = 2.
  • Muon lepton number \( (L_\mu) \) starts at 1 (muon) and ends at 0 - 1 (muon antineutrino) = 0.
  • Tau lepton number \( (L_\tau) \) remains unchanged at 0 throughout the process.
In this decay, all lepton numbers are conserved, confirming it aligns with lepton number conservation laws.
Tau Decay
A tau lepton, symbolized by \(\tau^-\), is another heavier cousin of the electron. It's part of the lepton family and can undergo a decay process.

In the decay \(\tau^-\rightarrow e^- + \overline{u}_e + \overline{u}_\tau\), the tau transforms into:
  • an electron \((e^-)\),
  • an electron antineutrino \((\overline{u}_e)\), and
  • a tau antineutrino \((\overline{u}_\tau)\).
Lepton number conservation applies again. Let's consider:
  • Electron lepton number \( (L_e) \) begins at 0 and changes to 1 (electron) - 1 (electron antineutrino) = 0.
  • Muon lepton number \( (L_\mu) \) starts and remains at 0 both before and after decay.
  • Tau lepton number \( (L_\tau) \) begins at 1 (tau) and results in 0 - 1 (tau antineutrino) = 0.
Thus, all lepton numbers are conserved in this tau decay, adhering to the rules of lepton number conservation.
Leptons in Particle Physics
Leptons are fundamental particles in physics. They include electrons, muons, and tau particles, each having a corresponding neutrino.

There are three types of lepton numbers in particle physics:
  • Electron lepton number \((L_e)\)
  • Muon lepton number \((L_\mu)\)
  • Tau lepton number \((L_\tau)\)
Each lepton family has a specific lepton number, and these numbers must be conserved in all nuclear and particle reactions.
Conservation of lepton number ensures that for each type of lepton participating in a reaction:
  • The number of these leptons minus the number of their corresponding antineutrinos remains constant.
  • This conservation maintains the balance and predictability in particle interactions.
  • It plays a crucial role in understanding processes such as particle decay and interactions.
Understanding this principle is essential in predicting and analyzing outcomes in particle physics, ensuring that reactions follow the physical laws of the universe.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Each of the following reactions is missing a single particle. Calculate the baryon number, charge, strangeness, and the three lepton numbers (where appropriate) of the missing particle, and from this identify the particle. (a) \(p + p \rightarrow p + \Lambda^0 + \)? ; (b) \(K^- + n \rightarrow \Lambda^0 +\) ? ; (c) \(p + \overline {p} \rightarrow n + \)?; (d) \(\overline{\nu} _\mu + p \rightarrow n +\)?

The spectrum of the sodium atom is detected in the light from a distant galaxy. (a) If the 590.0-nm line is redshifted to 658.5 nm, at what speed is the galaxy receding from the earth? (b) Use the Hubble law to calculate the distance of the galaxy from the earth.

Calculate the threshold kinetic energy for the reaction \(p + p \rightarrow p + p + K^+ + K^-\) if a proton beam is incident on a stationary proton target.

Which of the following reactions obey the conservation of baryon number? (a) \(p + p \rightarrow p + e^+\); (b) \(p + n \rightarrow 2e^+ + e^-\); (c) \(p \rightarrow n + e^- + \overline{\nu}_e\); (d) \(p + \overline{p} \rightarrow 2\gamma\).

A proton and an antiproton annihilate, producing two photons. Find the energy, frequency, and wavelength of each photon (a) if the p and \(\overline{p}\) are initially at rest and (b) if the p and \(\overline{p}\) collide head-on, each with an initial kinetic energy of 620 MeV.
See all solutions

Recommended explanations on Physics Textbooks

Mechanics and Materials

Read Explanation

Medical Physics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Electromagnetism

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.